# Stored data for newform 162.4.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "162.4.a.e", "space_label": "162.4.a", "level": 162, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014398576591010, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 2300492955764654337, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [9, 12, 1]]], "qexp_display": "q-2q^{2}+4q^{4}+(-6+\\beta )q^{5}+(8-2\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2592, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 9.55830942092998, "hecke_ring_index": 3, "level_radical": 6, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [162, 1, [83], [1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.662", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.880", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1]], "trace_display": [-4, 0, -12, 16], "traces": [0, 2, -4, 0, 8, -12, 0, 16, -16, 0, 24, -36, 0, 10, -32, 0, 32, -120, 0, -8, -48, 0, 72, -180, 0, -124, -20, 0, 64, -324, 0, -248, -64, 0, 240, -204, 0, -434, 16, 0, 96, -192, 0, -608, -144, 0, 360, 384, 0, -342, 248, 0, 40, 408, 0, -216, -128, 0, 648, 1008, 0, 742, 496, 0, 128, 696, 0, -104, -480, 0, 408, 1140, 0, 850, 868, 0, -32, 576, 0, -440, -192, 0, 384, -264, 0, 1314, 1216, 0, 288, -768, 0, -1432, -720, 0, -768, -1140, 0, -764, 684, 0, -496, 1416, 0, -2120, -80, 0, -816, -168, 0, 1642, 432, 0, 256, 768, 0, 864, -1296, 0, -2016, -2148, 0, 1442, -1484, 0, -992, 1596, 0, -824, -256, 0, -1392, -804, 0, 2312, 208, 0, 960, -3240, 0, 1528, -816, 0, -2280, -6228, 0, 2322, -1700, 0, -1736, -4140, 0, -1904, 64, 0, -1152, 3432, 0, 1102, 880, 0, 384, -1008, 0, -128, -768, 0, 528, 876, 0, 6240, -2628, 0, -2432, -3900, 0, 304, -576, 0, 1536, 6528, 0, 4228, 2864, 0, 1440, 2496, 0, -2592, 1536, 0, 2280, -1212, 0, 3190, 1528, 0, -1368, -3684, 0, 280, 992, 0, -2832, -3348, 0, -1224, 4240, 0, 160, 9648, 0, -3392, 1632, 0, 336, 3972, 0, -5872, -3284, 0, -864, 7716, 0, -3128, -512, 0, -1536, -588, 0, 3298, -1728, 0, 2592, 4944, 0, -4248, 4032, 0, 4296, 7896, 0, 610, -2884, 0, 2968, 324, 0, -16672, 1984, 0, -3192, -3444, 0, 4968, 1648, 0, 512, -9168, 0, -3256, 2784, 0, 1608, 5808, 0, 1656, -4624, 0, -416, 3756, 0, -11480, -1920, 0, 6480, 7416, 0, -140, -3056, 0, 1632, -5328, 0, 8968, 4560, 0, 12456, 3216, 0, 3908, -4644, 0, 3400, -5220, 0, -4320, 3472, 0, 8280, -3924, 0, -5512, 3808, 0, -128, -3480, 0, 8824, 2304, 0, -6864, -13512, 0, 1078, -2204, 0, -1760, 2172, 0, 2808, -768, 0, 2016, -12588, 0, -9692, 256, 0, 1536, 6960, 0, 1720, -1056, 0, -1752, -6828, 0, 1204, -12480, 0, 5256, -11088, 0, -4768, 4864, 0, 7800, -4740, 0, 3364, -608, 0, 1152, -14688, 0, -6408, -3072, 0, -13056, 1188, 0, 12450, -8456, 0, -5728, 84, 0, -10112, -2880, 0, -4992, -4944, 0, -3428, 5184, 0, -3072, 3672, 0, 232, -4560, 0, 2424, -12468, 0, -4968, -6380, 0, -3056, 15240, 0, 8424, 2736, 0, 7368, 5340, 0, -11858, -560, 0, -1984, -984, 0, 25976, 5664, 0, 6696, 8676, 0, -6878, 2448, 0, -8480, 4608, 0, -1656, -320, 0, -19296, 17256, 0, -11414, 6784, 0, -3264, 312, 0, 3992, -672, 0, -7944, 2760, 0, -626, 11744, 0, 6568, 5472, 0, 4792, 1728, 0, -15432, 1680, 0, 9414, 6256, 0, 1024, 8784, 0, 22464, 3072, 0, 1176, 14100, 0, -9230, -6596, 0, 3456, 2520, 0, 5392, -5184, 0, -9888, -1176, 0, 14072, 8496, 0, -8064, 8352, 0, 14752, -8592, 0, -15792, 7188, 0, -3682, -1220, 0, 5768, 7608, 0, -1592, -5936, 0, -648, -21348, 0, 23598, 33344, 0, -3968, 8256, 0, 30064, 6384, 0, 6888, -7992, 0, 1008, -9936, 0, -3296, -120, 0, -3568, -1024, 0, 18336, 15960, 0, 8640, 6512, 0, -5568, 5424, 0, 26032, -3216, 0, -11616, 36264, 0, -7270, -3312, 0, 9248, -34224, 0, -13032, 832, 0, -7512, 19980, 0, -33086, 22960, 0, 3840, -19248, 0, 18760, -12960, 0, -14832, -7020, 0, -8920, 280, 0, 6112, -14700, 0, 1496, -3264, 0, 10656, -21264, 0, -18702, -17936, 0, -9120, 38856, 0, -704, -24912, 0, -6432, 13752, 0, -29930, -7816, 0, 9288, 4368, 0, -40176, -6800, 0, 10440, -33108, 0, -41776, 8640, 0, -6944, -45984, 0, 24120, -16560, 0, 7848, 1080, 0, 18526, 11024, 0, -7616, 6900, 0, -4160, 256, 0, 6960, -25296, 0, 11164, -17648, 0, -4608, -19776, 0, 12928, 13728, 0, 27024, -15756, 0, -286, -2156, 0, 4408, 24852, 0, -42320, 3520, 0, -4344, -4452, 0, -25902, -5616, 0, 1536, -43272, 0, 33736, -4032, 0, 25176, -11844, 0, -31968, 19384, 0, -512, -30456, 0, 20592, -3072, 0, -13920, 13476, 0, -8690, -3440, 0, 2112, -22944, 0, 27648, 3504, 0, 13656, -21132, 0, -39482, -2408, 0, 24960, -21480, 0, -12160, -10512, 0, 22176, 11376, 0, 29862, 9536, 0, -9728, 59496, 0, -2840, -15600, 0, 9480, 5304, 0, -14616, -6728, 0, 1216, 12540, 0, 4112, -2304, 0, 29376, -7680, 0, -19070, 12816, 0, 6144, 14544, 0, 21600, 26112, 0, -2376, -25812, 0, -23440, -24900, 0, 16912, 15552, 0, 31216, 11456, 0, -168, 40044, 0, 7780, 20224, 0, 5760, 61488, 0, -24008, 9984, 0, 9888, -13920, 0, 9234, 6856, 0, -10368, 26736, 0, -48080, 6144, 0, -7344, -2184, 0, 5476, -464, 0, 9120, -1176, 0, 31928, -4848, 0, 24936, 29232, 0, -14858, 9936, 0, 12760, 972, 0, -7952, 6112, 0, -30480, 53040, 0, -23976, -16848, 0, -5472, 6672, 0, 23152, -14736, 0, -10680, 34332, 0, 17318, 23716, 0, 1120, 7428, 0, -44424, 3968, 0, 1968, -56772, 0, 14040, -51952, 0, -11328, 36024, 0, 22864, -13392, 0, -17352, 4224, 0, -4696, 13756, 0, -4896, 7212, 0, 6904, 16960, 0, -9216, -19740, 0, -34748, 3312, 0, 640, 1512, 0, 32328, 38592, 0, -34512, -8652, 0, 6356, 22828, 0, -13568, -29880, 0, -19568, 6528, 0, -624, 39492, 0, 69772, -7984, 0, 1344, 26520, 0, 20248, 15888, 0, -5520, 11004, 0, 25506, 1252, 0, -23488, -13680, 0, -104848, -13136, 0, -10944, 25188, 0, -34274, -9584, 0, -3456, -43296, 0, 4744, 30864, 0, -3360, -54660, 0, 12200, -18828, 0, -12512, 41232, 0, -51912, -2048, 0, -17568, 53784, 0, 20664, -44928, 0, -6144, -18024, 0, 20800, -2352, 0, -28200, -18372, 0, 30672, 18460, 0, 13192, -37968, 0, 6664, -6912, 0, -5040, 11748, 0, 28204, -10784, 0, 10368, -69672, 0, 39384, 19776, 0, 2352, 30780, 0, 48670, -28144, 0, -16992, 12996, 0, 26784, 16128, 0, -16704, -24564, 0, 76826, -29504, 0, 17184, -58392, 0, 9000, 31584, 0, -14376, -46764, 0, 41154, 7364, 0, 2440, -40524, 0, 38272, -11536, 0, -15216, -47124, 0, -16720, 3184, 0, 11872, -38160, 0, -24624, 1296, 0, 42696, -37032, 0, 30474, -47196, 0, -66688, 53424, 0, -11264, 7936, 0, -16512, -15504, 0, 4198, -60128, 0, -12768], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "162.4.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-2, 0], [0, 0], [4, 0], [-6, 1], [0, 0], [8, -2], [-8, 0], [0, 0], [12, -2], [-18, -8], [0, 0], [5, 14], [-16, 4], [0, 0], [16, 0], [-60, 11], [0, 0], [-4, -22], [-24, 4], [0, 0], [36, 16], [-90, -4], [0, 0], [-62, -12], [-10, -28], [0, 0], [32, -8], [-162, 7], [0, 0], [-124, 36], [-32, 0], [0, 0], [120, -22], [-102, 20], [0, 0], [-217, -2], [8, 44], [0, 0], [48, -8], [-96, -44], [0, 0], [-304, 6], [-72, -32], [0, 0], [180, 8], [192, -36], [0, 0], [-171, -32], [124, 24], [0, 0], [20, 56], [204, 76], [0, 0], [-108, 30], [-64, 16], [0, 0], [324, -14], [504, 32], [0, 0], [371, 18], [248, -72], [0, 0], [64, 0], [348, -79], [0, 0], [-52, -138], [-240, 44], [0, 0], [204, -40], [570, 8], [0, 0], [425, 96], [434, 4], [0, 0], [-16, -88], [288, -28], [0, 0], [-220, 50], [-96, 16], [0, 0], [192, 88], [-132, -60], [0, 0], [657, -126], [608, -12], [0, 0], [144, 64], [-384, 89], [0, 0], [-716, 102], [-360, -16], [0, 0], [-384, 72], [-570, 128], [0, 0], [-382, 56], [342, 64], [0, 0], [-248, -48]]}